Originally Written: September 2008
The transfer market in professional football was particularly buoyant in the summer of 2008. And amongst the most prominent traders were the top English Premiership clubs such as Manchester United and Chelsea. The FA Premier League has the highest revenues of any domestic football league in the world, grossing £1.5 billion in revenues in season 2006/07. The top Premiership clubs also compete in the highly lucrative UEFA Champions League. So not surprisingly the top English Premiership clubs are able to outbid most of their rivals to attract the best players in the world by offering wages in excess of £100,000 per week for the top earners. But is there any economic justification for Manchester United paying a transfer fee of £30.75 million to Tottenham Hotspur for the striker, Dimitar Berbatov or Manchester City paying £32.5 million to Real Madrid to obtain the services of the Brazilian international, Robinho?
What does economic and financial analysis have to say about the valuation of professional footballers? From an economic and financial perspective professional footballers are complex productive assets who are expected to provide a flow of services both on and off the field over the period of their employment contract. Just as with other productive assets, there are two basic methods of valuing professional footballers – benchmark (or comparative) valuation and fundamental valuation. Benchmark valuation determines the market valuation of a specific asset by comparison with the observed market values of similar assets that have been recently traded. It is an anchor-and-adjustment method of valuation in which recent market transactions provide an “anchor” to be adjusted given the specific characteristics of the particular asset being valued. By contrast, fundamental valuation attempts to calculate the expected future net benefits to be received from using the asset productively.
One widely used method of benchmark valuation is a valuation ratio in which the market value of an asset is expressed relative to an appropriate indicator of asset quality. To estimate the market value of asset using a valuation ratio, you need to identify a key characteristic of the asset and then calculate the average ratio between market value and that asset characteristic for similar types of assets that have been recently traded. Valuation ratios are often employed to provide an initial estimate of the market value of company equity. The two most popular corporate valuation ratios are the price-earnings ratio (i.e. market equity value relative to profit after tax) and the market-to-book ratio (i.e. market equity value relative to the book value of the company equity as stated in the balance sheet).
However in trying to value professional footballers it is difficult to identify a single indicator of asset quality. In this case benchmark valuation needs to employ a multivariate method that allows for multiple indicators of asset quality. Effectively this type of asset valuation is a form of hedonic pricing in which the asset is viewed as consisting of a set of characteristics, with each characteristic having an implicit (or hedonic) price. Statistical techniques such as regression analysis can be used to decompose observed asset market values into a linear combination of individual asset characteristics with the estimated coefficients representing the implicit prices of each characteristic. Several published studies of the football transfer market have shown that there is a high degree of statistical predictability in transfer fees. For example, a study published by Gerrard and Dobson (2000) analysed 1,350 player transfers between English professional football clubs over the period 1990 – 1996. Gerrard and Dobson found that around 80 per cent of the variation between individual transfer fees could be explained statistically. Although the final regression model contained around 70 explanatory variables, effectively these can be grouped into four types of characteristics – the quality of the player, the size and league status of the selling club, the size and league status of the buying club, and general market conditions. The key indicators of player quality are age, career league appearances, current appearance rates, scoring rates and international recognition. It is not really surprising that there is such a high degree of statistical predictability in football transfer fees despite the popular belief to the contrary. The high statistical predictability of football transfer fees can be interpreted as evidence that football clubs tend to benchmark against recent deals when valuing players. But benchmarking in this way can create a bootstrapping property in which market values pull themselves up (or down) as the value of each transaction is justified by the value of every other similar transaction. In economic terms benchmark valuation is just about setting relative prices. The Gerrard and Dobson study shows that the transfer market is very systematic in setting relative prices. The issue remains whether or not the absolute level of prices in the football transfer market is appropriate. Are transfer fees correctly anchored? To answer that question requires consideration of fundamental valuation techniques.
Fundamental valuation involves calculating the value of the expected flow of net benefits to accrue to the holder of an asset. In investment analysis the principal method of fundamental valuation is discounted cash flow (DCF) analysis in which the expected future net cash flows are converted to their present value equivalent (i.e. what you would pay now for the right to receive a risky cash flow at some specified time in the future) by discounting the future cash flows using a discount rate that allows for the delay, risk and expected future inflation. In the economic analysis of factor returns, fundamental valuation is measured by marginal revenue product (MRP). MRP is best seen as the measure of economic value provided by a factor of production over a single period whereas DCF measures the economic value provided over the whole working life of an asset (or over the length of an employment contract for a professional footballer).
The MRP of a professional footballer requires estimating the expected incremental cash flows accruing to the club as a consequence of signing that player. Broadly speaking there are two types of revenue streams that a player can generate. Firstly, there are the revenue streams associated with the player’s on-the-field contribution to team performance. Team revenues tend to be “win-elastic”. Winning teams tend to attract more spectators, generating higher match-day revenues. Media revenues can also be win-elastic with bigger viewing audiences for the more successful teams. Sponsorship and merchandising revenues also tend to be higher for more successful teams. But a player’s value will also depend on his expected image value off-the-field. Star players can generate greater revenues by virtue of being star players irrespective of their actual impact on team performance. Glamour as well as glory makes money in professional team sports which when all is said and done are part of the entertainment industry. So from the economic perspective the fundamental value of a professional footballer can be stated as:
MRP = (MPC x MWR) + PIV
where MPC is the (expected) marginal playing contribution, MWR is the marginal win revenue and PIV is the player image value. Calculating a player’s value requires an estimate of the incremental impact of the player on the team performance, an estimate of the sensitivity of the team’s revenues to team performance and an estimate of the off-the-field marketing value of the player.
The first empirical investigation of the MRP of a professional athlete was published by Scully in 1974. Scully estimated the MRPs of professional baseball players. He developed a two-stage procedure. Using multiple regression analysis, Scully first estimated a statistical model of team performance to derive the relationship between team win percentage and team hitting and pitching records. This allowed Scully to calculate how much of the team win percentage had been contributed by each individual hitter and pitcher to determine each player’s MPC. Next Scully estimated a team revenue model to determine the incremental revenue value (i.e. MWR) of a one base point increase in the team win percentage. Taken together these two regressions allowed Scully to estimate the MRP of a baseball player’s on-the-field contribution. (Scully ignored player image values which was justifiable given that commercial exploitation of image rights was still in its infancy in the late 1960s.) Using his regression estimates, Scully estimated that the MRP of an average hitter or pitcher in major league baseball in the late 1960s was around $260,000. However player salaries at the time were only around one-fifth of this due to the monopsonistic conditions in the players’ labour market with players effectively restricted to bargaining only with their current team. Player salaries only moved towards parity with player MRP in major league baseball when free agency was introduced for senior players in the late 1970s.
Baseball lends itself very well to this type of economic analysis because the contributions of individual players are highly separable in striking-and-fielding games. Indeed one major league baseball team, the Oakland Athletics, has successfully incorporated the statistical approach into decisions on player recruitment, remuneration and even field tactics as a way of trying to close the gap with big-market rivals such as the New York Yankees who typically spend more than three times more on player salaries that the small-market Athletics. The story of how Oakland’s General Manager, Billy Beane, revolutionised the team’s approach to player scouting is told in the bestselling book, Moneyball: The Art of Winning an Unfair Game, by Michael Lewis (2003). One way in which Oakland was able to buy wins more cheaply that its rivals was by exploiting market inefficiency in the valuation of hitters. As Hakes and Sauer (2006) show, the conventional performance measures used by teams to value hitters were not the best statistical predictors of team performance. Billy Beane relied on a better statistical measure of hitting performance, on-base percentage, which had been ignored by other teams. However, after the publication of Moneyball the market inefficiency disappeared and on-base percentage became the strongest predictor of player salaries.
Moneyball has stimulated considerable interest in other sports such as football but there are a number of difficulties in adapting the statistical methods of Scully and Oakland to complex invasion team sports such as football, rugby, hockey and basketball. In these sports individual player performance is much less separable. There are three problems to be resolved to be able to estimate the MRP of players in complex invasion team sports – the tracking problem, the weighting problem and the attribution problem. The tracking problem refers to the identification, categorisation and enumeration of different types of player actions. Historically performance statistics in complex invasion team sports were limited to appearance and scoring data. The advent of video analysis and image recognition software has resolved the tracking problem. Top Premiership football clubs use tracking systems such as ProZone and Amisco to track all player actions on the ball (e.g. passing, tackling and shooting) as well as the direction, distance and speed of all player movements. The raw data is now available to determine player contributions. This leads to the weighting problem of determining the significance of different player actions to match outcomes. The weighting problem can be resolved by the use of multivariate statistical techniques such as regression analysis and structural modelling within an appropriate conceptual model of the interrelationships between player actions and match outcomes. Statistically-derived indices of player performance are now available in most professional team sports. In English professional football the two most widely quoted player performance measures are the Opta Index and the Actim Index. Finally the attribution problem involves the allocation of individual contributions to joint and interdependent actions such as scrimmaging and tackling in rugby when the contributions of individual players cannot be separately identified and weighted by purely statistical means. These attribution problems can largely be resolved by the expert judgment of coaches.
Summing up, it seems clear that the application of economic and financial analysis to the valuation of professional footballers is now feasible. Video and tracking technologies can provide extensive data on player match contributions. Sport science and coaching experts can provide appropriate conceptual models of the relationship between player actions and match outcomes. Economic analysis can provide both a theoretical understanding of the fundamental value of players and the empirical methods to estimate these values. But professional football clubs have yet to embrace this approach to asset valuation that is common place in investment decisions by firms in most other industries. Just as in major league baseball pre-Moneyball there is a deep rooted belief in professional football that player valuation is inherently subjective and a matter of sporting judgment by football managers. As a consequence player values are largely determined by benchmarking against the (subjective) valuations of other managers as observed in recent transfer fees and wage contracts. It is exactly this type of opportunity that the Oakland Athletics exploited to identify playing talent whose productive value in terms of win contribution exceeded their market salary value. Nothing persuades as much as success. Football will embrace the Moneyball approach when a football club emulates Oakland by achieving a sustainable competitive advantage through the application of rigorous analysis to the valuation of players.
References
B. Gerrard and S. Dobson, ‘Testing for monopoly rents in the market for playing talent’, Journal of Economic Studies, vol. 27 (2000), pp. 142-164.
J. K. Hakes and R. D. Sauer, ‘An economic evaluation of the Moneyball hypothesis’, Journal of Economic Perspectives, vol. 20 (2006), pp. 173-185.
M. Lewis, Moneyball: The Art of Winning an Unfair Game, Norton, 2003.
G. W. Scully, ‘Pay and performance in Major League Baseball’, American Economic Review, vol. 64 (1974), pp. 915-930.
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